As a member of the Institute of Medicine since 1999, much of Brinkley's research has focused on studies of the molecular regulation of the cell cycle and mitosis with emphasis on genomic instability in human cancers. He is noted for pioneering work utilizing electron microscopy for the study of cultured human cells and for developing methods to localized proteins and nucleic acids in cells by fluorescence microscopy.

A native Texan, Brinkley grew up in East Texas and went to high school in Willis. He received his undergraduate and master's degrees from Sam Houston State University in Huntsville and his doctorate from Iowa State University. He began his research in cancer during as postdoctoral fellowship at The University of Texas MD Anderson Cancer Center in Houston.

TAMEST was founded in 2004 to provide broader recognition of the state's top achievers in medicine, engineering and science, and to build a stronger identity for Texas as an important destination and center of achievement in these fields. Members include Texas Nobel Laureates and more than 200 members of the National Academies. TAMEST brings the state's top scientific, academic and corporate minds together to further position Texas as a national research leader. TAMEST also works to foster the next generation of scientists and to increase the awareness and communication among the state's best and brightest about research priorities for the future.